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Data Analysis: Part 2 Lesson 7.1 & 7.2 1/11-12/12

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Data Analysis: Part 2 MM2D1. Using sample data, students will make informal inferences about population means and standard deviations. a. Pose a question and collect sample data from at least two different populations. b. Understand and calculate the means and standard deviations of sets of data. c. Use means and standard deviations to compare data sets.

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Data Analysis: Part 2 d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

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Data Analysis: Part 2 Solve for the mean, median, mode, range, quartile for the following data set. 71, 70,68,74,73,67,66,75,74,68,70,75,73,73,72, 67, 68,63, 72, 70 **Homework/Answers**

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Data Analysis: Part 2 EQ: What is a variance? What is standard deviation? Today you will begin to learn about data analysis as we learn about variance and standard deviation!!

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Data Analysis: Part 2 How to create a box and whisker plot Step 1: Place the elements of the data set in numerical order Step 2: Find median of the entire set (Q2) Step 3: Find the median of lower quartile (Q1) and median of upper quartile (Q3)**If the number of data in the data set is EVEN include the middle values to compute the Q1 & Q3 medians; If data set id ODD DO NOT include the middle value for the entire data set*** Step 4: Identify the range value (maximum and minimum elements) of data set **The box provides you with the central value of the data set; The whiskers represents the minimum and maximum values of the data set**

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Data Analysis: Part 2 Subjective vs. Random Sample Example: Height, Age, Food

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Data Analysis: Part 2 Examples: Create a box and whisker plot for following data sets Data set: 16, 25, 40, 72, 53, 84, 66, 42, 51, 22, 35, 17, 26, 48, 36, 59, 60, 64, 29, 71 Data set: 5.2, 9.1, 4.5, 1.3, 5.9, 8.4, 6.7,4.2,6.0,9.0, 10.5, 2.8, 4.7, 5.5, 4.5

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Data Analysis: Part 2 RANDOM NUMBER GENERATOR- a machine or program that will generate random numbers Ex: Random Number Table, Random Number Option on Calculator

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Data Analysis: Part 2 Steps to find a Random Numbers using TI-30XIIS Calculator: Press PRB Use R arrow until come to RANDI Press Enter Press number want to start with comma number want to stop with **Values will be include within parenthesis and to get comma press 2 nd close parenthesis button**

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Data Analysis: Part 2 Examples: Example#1 Random numbers for the interval [1, 100] Example #2 Random numbers for the interval [5, 20] Example #3 Random numbers for the interval (20, 40) Example #4 Random numbers for the interval (18, 36)

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Data Analysis: Part 2 Fact: The distribution a set of data can be measured using the population distribution or a sample distribution Fact: The population distribution is categorized by the mean and standard deviation

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Data Analysis: Part 2

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IMPORTANT FACT: The mean, variance, and standard deviation of a random sample can fairly accurately characterize the whole population!!!!!!!!!!!

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Data Analysis: Part 2 Calculate the variance and standard deviation of the following data set Example #1 Prices of cars at a dealership: 12,000 14,500 22,000 17,750 13,450 16,875 56,000 12,750 13,650 14,735

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Data Analysis: Part 2 Calculate the variance and standard deviation of the following data set Example #1 Plant Heights (in centimeters) 10 14 11 12 10 13 13 12 13 12

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Data Analysis: Part 2 Calculate the variance and standard deviation of the following data set Example #1 Scores on an English test: 54 68 53 75 42 48 70 58 64 63

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Data Analysis: Part 2 Homework: Skills pg. 463-467 Problem Set #1 (2-5) (7-10) (12-22)

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Data Analysis: Part 2 Activation: Solve for the mean, median, mode, range, quartile for the following data set. 71, 70,68,74,73,67,66,75,74,68,70,75,73,73,72, 67, 68,63, 72, 70 Instruction: Notes on Box and Whisker Plot, Variance, and Standard Deviation Work: Complete Guided Examples on Box and Whisker Plot, Variance, and Standard Deviation Assessment: Unit 4 Test Summary: Write the definition of variance and standard deviation

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